The present invention relates in general to mass flow measuring techniques and, in particular to a new and useful apparatus and method of measuring mass flow rate of the fluid utilizing two spaced apart tubes each meant for carrying about one half of the flow, which tubes are forced to oscillate between fixed points in order to impart a reciprocating angular rotation to the tubes.
Devices are known which utilize the effect of angular motion on a moving fluid to directly measure mass flow. See for example, U.S. Pat. No. 2,865,201 issued Dec. 23, 1958 to Roth and U.S. Pat. No. 3,355,944 issued Dec. 5, 1967 and U.S. Pat. No. 3,485,098 issued Dec. 23, 1969 to Sipin.
U.S. Pat. No. 4,109,524 issued Aug. 29, 1978 to Smith, discloses an apparatus and method for measuring mass flow rate through a conduit by reciprocating a section of the conduit to produce longitudinal angular rotation of that section. Linkages are connected to the section both for reciprocating it and for measuring a force exerted on the section which force is due to an apparent force produced by mass flow through the conduit section. A direct measurement can thus be taken of the mass flow rate in this manner.
To understand how mass flow rate can be measured using the effects of this force, reference is now made to FIG. 1 which shows an arrangement of vectors on an X, Y, Z coordinate system.
When a moving mass m with a velocity vector v is acted upon by a force that causes angular velocity w about some axis, a force F.sub.c is observed such that: F.sub.c =2mw.times.v
If a tube for carrying a fluid, shown at 10 in FIG. 1, is rotated in the F.sub.c -v plane, in the clockwise direction shown by arrow 12, this causes an angular velocity w as shown in FIG. 1. If however, rather than rotating conduit 10 in one direction shown by arrow 12, the conduit is caused to oscillate back and forth about its pivot which is shown at 16, the magnitude and polarity of the angular velocity w will also oscillate and, therefore, the magnitude and polarity of the force F.sub.c will oscillate proportionately.
For any point along the tube, for example the point 14, a displacement vector can be represented for small amplitudes as lying along the Y-axis only. As the flow tube 10 is forced to oscillate by a sinusoidal driver about its pivot point 16 with very small amplitude, and with the point 14 far from the pivot point 16, then the magnitude of its displacement, velocity and acceleration vectors can be represented by a graph which is shown at FIG. 2. The displacement of point 14 along the Y-axis is shown by the solid line 20. The velocity v of the point 14 is shown by the dash double dot line 22. This is in the units of inches/second and represents dy/dt.
Acceleration A is shown by the solid line 26 and represents the second derivative of displacement with respect to time, in the units inches/second.sub.2 and represents d.sup.2 y/dt.sup.2.
If there is a fluid flowing in the tube, a force F.sub.c =2mw.times.v, acting on the flowing mass, will also be developed. By Newton's third law it will develop an equal and opposite force -F.sub.c acting on the tubing itself and be acceleration A', with -F.sub.c and A' along the Y-axis. The magnitude of A' is shown by the dotted line 28. From the definition for the force -F.sub.c set forth above, it can be seen that this force is proportional to the velocity of the point 14, which is 90.degree. out of phase with the acceleration due to the driving force applied to the conduit. The resultant force acting at the point 14 will be the sum of the driving and the force -F.sub.c, with these two forces 90.degree. our of phase. The dot-dash curve 24 represents the sum associated with the accelerations A plus A' which is proportional to the sum of the driving force and the force -F.sub.c. A phase difference of .phi. between the original driving acceleration and the resultant summed acceleration will, therefore, be a direct measurement of the force -F.sub.c which is directly proportional to the mass flow rate.
If the driving force is sinusoidal, then its displacement, velocity and acceleration will likewise be sinusoidal and vary by 90.degree. and 180.degree. respectively. This allows the phase difference .phi. to be equal regardless of whether it is measured relative to the displacement, velocity or acceleration functions of the drive force versus resultant drive force plus the force -F.sub.c.